Lattice distortions perpendicular to the surface in thin surface layers of ion-implanted (111) silicon crystals have been mapped as a function of depth and lateral position with resolutions of 0.05 and 0.65gm, respectively. X-ray triple-crystal diffractometry data were collected near the fundamental 111 and satellite reflections from samples with periodic superstructure modulations in the lateral direction. 300 keV B + ions implanted through surface mask windows are found to produce lattice distortions in a very thin layer of 0.15 gm thickness at 1.05 gm depth below the surface, with interplanar lattice spacings normal to the surface increased by several parts in 104 . The distortions are appreciably extended in the lateral direction, suggesting diffusion of the ions. A 0.5 gm-thick thermaloxide strip is found to contract the interplanar spacing of substrate silicon crystal under the strip region by a few parts in 104, while the strain field created by the parallel oxide edges extends beyond a depth of 3 Bm. A practical procedure is also described for arriving at a solution of the phase problem in the case of a strain field involving heavily distorted layers.
The crystal structure of magnesium boron nitride in the low-pressure phase, Mg3BN3(L), has been solved ab initio from X-ray powder data. The cell is hexagonal (space group P63/mmc, Z = 2) with a = 3.54453 (4), c = 16-03536 (30)/k. Initial positional parameters for the Mg atoms were obtained from Patterson functions generated by 50 integrated intensities derived from a whole-powder pattern decomposition. The remaining atoms were located by trial-and-error model building, followed by Rietveld refinements (R,p = 8.5%). The structure can be described as consisting of ABB'BACC'CA... layers perpendicular to the c axis with linear N-~-B~N molecular anions at position A, Mg 2+ at positions B and C and Mg 2+ with three coordinating N atoms at positions B' and C', although Mg3BN3(L) is not a layer compound. A very similar structure has also been obtained by applying standard direct methods to the same intensity data. A high-quality electrondensity map has been calculated from the structurefactor data using the maximum-entropy method.
The strain distribution in a Si 0.9 Ge 0.1 /Si superlattice is determined from x-ray diffractometry data with a 25 Å depth resolution. A logarithmic dispersion relation is used to determine the phase of the structure factor with information available a priori on the sample structure. Phase information is obtained from the observed reflection intensity via a logarithmic Hilbert transform and the a priori information is used to select the zeros to be included in the solution. The reconstructed lattice strain profile clearly resolves SiGe and Si layers of 90-160 Å thickness alternately stacked on a silicon substrate. The SiGe layer is found to have a lattice spacing in the surface-normal direction significantly smaller than predicted by Vegard's law. The result gives simulated rocking-curve profiles in very good agreement with the observation. The apparent deviation from Vegard's law could be confirmed by chemical analysis.
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